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Popular >

integral from 0 to 1 of x(x^2+2)

Solution

\int_{0}^{1} x (x^{2} + 2) d x

Solution

\frac{5}{4}

+1

Decimal

1.25

Solution steps

\int_{0}^{1} x (x^{2} + 2) d x

Expand

x (x^{2} + 2) : x^{3} + 2 x

= \int_{0}^{1} x^{3} + 2 x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} x^{3} d x + \int_{0}^{1} 2 x d x

\int_{0}^{1} x^{3} d x = \frac{1}{4}

\int_{0}^{1} 2 x d x = 1

= \frac{1}{4} + 1

Simplify

\frac{1}{4} + 1 : \frac{5}{4}

= \frac{5}{4}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of x(x^2+2) ?
The integral from 0 to 1 of x(x^2+2) is 5/4